Microplane model for concrete with relaxed kinematic constraint

Abstract

In the paper, the microplane material model for concrete based on the relaxed kinematic constraint is presented. The model is aimed to be used for three-dimensional damage and fracture analysis of concrete and reinforced concrete structures in the framework of smeared crack approach. In the microplane model, the material is characterized by a relation between the stress and strain components on planes of various orientations. These planes may be imagined to represent the damage planes or weak planes in the microstructure, such as contact layers between aggregate pieces in concrete. The tensorial invariance restrictions need not be directly enforced. They are automatically satisfied by superimposing in a suitable manner the responses from all the microplanes. To realistically model concrete under compressive load, for each microplane, the total strain tensor has to be decomposed into the normal (volumetric and deviatoric) and shear strain component. It is shown that for dominant tensile load the decomposition of the normal microplane strain into volumetric and deviatoric part, together with the fact that the tensile strength of concrete is an order of magnitude smaller than it's compressive strength, leads to unrealistic model response. To keep the conceptual simplicity, the model is improved in the framework of the kinematic microplane theory, however, the kinematic constraint at the microplane level is relaxed. The proposed approach finds its physical background in the discontinuity of the strain field. It is demonstrated that the improved model correctly predicts the concrete response for dominant tensile load. The implementation of the initial anisotropy and the modeling of concrete for cyclic loading is also discussed. Comparison with a number of test data for different stress–strain histories shows a good agreement. The model has been recently implemented into a two- and three-dimensional finite element code and coupled with the localization limiter of local (crack band) and nonlocal integral type.